This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A191623 #19 Feb 16 2020 01:00:57
%S A191623 3,19,11251,2980024297506569894680811251
%N A191623 Primes of the form 1 + Product_{k=1..n} prime(k)^(2^(k-1)).
%C A191623 Primes of the form 1 + A191554(k), associated with positions k = 1, 2, 3, and 5 there. The next one (if it exists) occurs at k >= 15 and has > 53500 digits. [Edited by _R. J. Mathar_, Jun 17 2011 and _Joerg Arndt_, Jun 21 2011]
%C A191623 This connects A191554 and A191555, which are deeply about primes and monic polynomial irreducible by Eisenstein's Criterion, to primes by another way, connecting additive and multiplicative number theory analogously to the relationship in Primorial primes: A014545, n such that n-th Euclid number (A006862(n)) = 1 + (Product of first n primes) is prime.
%e A191623 a(1) = 1 + 2^1 = 1 + 2 = 3 is prime.
%e A191623 a(2) = 1 + (2^1 * 3^2) = 1 + 18 = 19 is prime.
%e A191623 a(3) = 1 + (2^1 * 3^2 * 5^4) = 1 + 11250 = 11251 is prime.
%t A191623 Select[Array[1 + Product[Prime[k]^(2^(k - 1)), {k, #}] &, 5], PrimeQ] (* _Michael De Vlieger_, Feb 15 2020 *)
%Y A191623 Cf. A000040, A191554.
%K A191623 nonn
%O A191623 1,1
%A A191623 _Jonathan Vos Post_, Jun 09 2011